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This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level 2, 2-quasi Einstein, generalized quasi-Einstein and Roter type manifold. Also, it is shown that the nature of the HBH spacetime is pseudosymmetric and it obeys several types of pseudosymmetries, such as, pseudosymmetry due to concircular, conformal and conharmonic curvature (i.e., F ⋅ F = L Q (g , F) for F = W , C , K with a smooth scalar function L), and it also possesses the relation R ⋅ R − L Q (g , C) = Q (S , R). It is engrossing to mention that the nature of energy momentum tensor of the HBH spacetime is pseudosymmetric. On the basis of curvature related properties, we have made a comparison among Reissner–Nordström spacetime, interior black hole spacetime and HBH spacetime. It is noteworthy to mention that the gravitational force of the point-like global monopole spacetime is much stronger than that of HBH spacetime. Also, it is shown that the HBH spacetime admits an almost η -Ricci soliton as well as an almost η -Ricci-Yamabe soliton. Finally, an elegant comparative study is delineated between the HBH spacetime and the point-like global monopole spacetime with respect to different kinds of symmetry, such as, motion, curvature collineation, curvature inheritance etc. • This paper aims to the study of curvature properties of Hayward black hole spacetime. • We have proved that the spacetime is an Ein(2), 2-quasi Einstein and Roter type. • Also shown that the nature of the spacetime obeys several types of pseudosymmetries. • We have compared Reissner–Nordström, interior black hole and HBH spacetime. • Also, the HBH spacetime admits an almost η -Ricci and almost η -Ricci-Yamabe solitons. [ABSTRACT FROM AUTHOR]

Gravitational weak lensing around a hairy black hole has been deeply studied in the presence of a plasma medium. The obtained results have shown that the effect of parameters a and l 0 on the deflection angle of light rays around the black hole in hairy spacetime is perceptible. With an increase of parameter a the deflection angle of photon orbits decreases, and the effect of plasma on the deflection angle is the opposite. Here, we discussed different types of plasma distributions: uniform ω e = c o n s t , Singular Isothermal Sphere medium, 1 / r and Non-Singular Isothermal gas sphere plasma. Additionally, The total magnification of the image source due to gravitational lensing has been also studied taking into account the effect of deviation parameter a and parameter l 0 related to hairy spacetime in the presence of plasma around the black hole. • Gravitational weak lensing around a hairy black hole has been deeply studied in the presence of a plasma medium. • The obtained results have shown that the effect of parameters a and I 0 on the deflection angle of light rays around the black hole in hairy spacetime is perceptible. • Here, we discussed different types of plasma distributions: uniform ω e = const , Singular Isothermal Sphere medium, 1 /r, and Non-Singular Isothermal gas sphere plasma. • The total magnification of the image source due to gravitational lensing has been also studied. [ABSTRACT FROM AUTHOR]